Geodesic
Upper bound for number of integral polynomials of four degree with given order of discriminants
Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 14-19

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In this paper we propose a new method for estimating the number of top-integral polynomials with given discriminates. We show asymptotically accurate height assessment in the case of polynomials of fourth degree. At the same time we used the methods of the metric theory of Diophantine approximations of dependent variables. 
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     author = {V. I. Bernik and O. N. Kemesh},
     title = {Upper bound for number of integral polynomials of four degree with given order of discriminants},
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V. I. Bernik; O. N. Kemesh. Upper bound for number of integral polynomials of four degree with given order of discriminants. Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 14-19. http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a1/